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The online catalog includes the most recent changes to courses and degree
requirements that have been approved by the Faculty Senate, including changes
that are not yet effective.
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### Courses

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The online catalog includes the most recent changes to courses and degree
requirements that have been approved by the Faculty Senate, including changes
that are not yet effective.
Courses showing two entries of the same number
indicate that the course information is changing. The most recently approved
version is shown first, followed by the older version, in gray, with its
last-effective term preceding the course title. Courses shown in gray with only
one entry of the course number are being discontinued.
Course offerings by term can be accessed by clicking on the term links when viewing a specific campus catalog.
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#### Mathematics (MATH)

100 Basic Mathematics 2 Course Prerequisite: A minimum ALEKS math placement score of 1%. Review of basic arithmetic and elementary algebra. No credit earned toward degree. S, F grading.

101 Intermediate Algebra 3 Fundamental algebraic operations and concepts. No credit earned toward degree.

103 Algebra Methods and Introduction to Functions 3 Course Prerequisite: MATH 100 with an S, MATH 101 with a C or better, or a minimum ALEKS math placement score of 40%. Fundamental algebraic operations and concepts, linear systems and inequalities, polynomial and rational functions, introduction to exponential and logarithmic functions.

105 [QUAN] Exploring Mathematics 3 Course Prerequisite: MATH 101, 103, or 251, each with a C or better, or STAT 212 with a C or better, or a minimum ALEKS math placement score of 45%. Nature and scope of modern mathematics, and its relationships to other disciplines.

106 College Algebra 3 Course Prerequisite: MATH 101 with a C or better, or MATH 103 with a C or better, or a minimum ALEKS math placement score of 70%. Graphs, properties and applications of polynomial, rational, exponential and logarithmic functions.

108 Trigonometry 2 Course Prerequisite: MATH 106 with a C or better. Graphs, properties and applications of trigonometric functions.

108 (Effective through Summer 2021) Trigonometry 2 Course Prerequisite: MATH 106 with a C or better. Graphs, properties and applications of trigonometric functions. Credit not normally granted for both MATH 108 and 107.

110 Mathematics Acceleration 1 (0-3) Course Prerequisite: A minimum ALEKS math placement score of 25%. Individualized instruction on mathematical skills to enhance the mathematical background necessary for success in one of MATH 103, 106, or 171. S, F grading.

111 Mathematics Tutorial for MATH 201 1 Course Prerequisite: Concurrent enrollment MATH 107. Student-centered group tutorial focusing on skill improvement for success in MATH 201. S, F grading.

115 Math 105 Tutorial 2 Tutorial for MATH 105 focusing on concept development and mastery; skill proficiency. S, F grading.

116 Math 106 Tutorial 2 Tutorial for MATH 106 focusing on concept development and mastery; skill proficiency. S, F grading.

140 [QUAN] Calculus for Life Scientists 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 171 or 202 except by department consent. Differential and integral calculus with emphasis on life science applications. By department consent, credit may be allowed for two of MATH 140, 171, or 202.

140 (Effective through Spring 2021) [QUAN] Calculus for Life Scientists 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 171 or 202 except by department consent. Differential and integral calculus with emphasis on life science applications. By department consent, credit may be allowed for two of MATH 140, 171, or 202.

171 [QUAN] Calculus I 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 83%. Enrollment not allowed if credit already earned for MATH 140 or 202 except by department consent. Differential and integral calculus of one variable with associated analytic geometry. By department consent, credit may be allowed for two of MATH 140, 171, or 202.

171 (Effective through Spring 2021) [QUAN] Calculus I 4 (3-3) Course Prerequisite: MATH 106 with a C or better and MATH 108 with a C or better, or a minimum ALEKS math placement score of 83%. Enrollment not allowed if credit already earned for MATH 140 or 202 except by department consent. Differential and integral calculus of one variable with associated analytic geometry. By department consent, credit may be allowed for two of MATH 140, 171, or 202.

172 Calculus II 4 (3-3) Course Prerequisite: MATH 171 with a C or better. Techniques and applications of one-variable calculus; estimations; series, derivative of a vector function. Credit not granted for both MATH 172 and 182.

182 Honors Calculus II 4 (3-3) Course Prerequisite: MATH 171 with a C or better; by department permission only. Single variable calculus, series, with emphasis on conceptual development and problem solving. Credit not granted for both MATH 172 and 182.

201 Mathematics for Business and Economics 3 Course Prerequisite: MATH 101 with a C or better, MATH 103 with a C or better, or a minimum ALEKS math placement score of 65%. Mathematical analysis using polynomial, exponential, and logarithmic functions; linear systems, linear programming and mathematics of finance, for business/economic applications and modeling.

202 [QUAN] Calculus for Business and Economics 3 Course Prerequisite: MATH 106 with a C or better, MATH 201 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 140 or 171 except by department consent. Differential calculus of the polynomial, exponential, and logarithmic functions; focus on unconstrained and constrained optimization, single and partial differentiation. By department consent, credit may be allowed for two of MATH 140, 171, or 202.

202 (Effective through Spring 2021) [QUAN] Calculus for Business and Economics 3 Course Prerequisite: MATH 106 with a C or better, MATH 201 with a C or better, or a minimum ALEKS math placement score of 80%. Enrollment not allowed if credit already earned for MATH 140 or 171 except by department consent. Differential calculus of the polynomial, exponential, and logarithmic functions; focus on unconstrained and constrained optimization, single and partial differentiation. By department consent, credit may be allowed for two of MATH 140, 171, or 202.

216 Discrete Structures 3 Course Prerequisite: MATH 108 with a C or better, or MATH 140, 171, 172, 182, or MATH 202 or concurrent enrollment. Discrete mathematics, trees, graphs, elementary logic, and combinatorics with application to computer science. Recommended preparation: Programming course.

220 Introductory Linear Algebra 2 Course Prerequisite: MATH 171 or concurrent enrollment. Enrollment not allowed if credit already earned for MATH 225 or 230. Solving linear systems, matrices, determinants, subspaces, eigenvalues, orthogonality. Credit not granted for more than one of MATH 220, 225, and 230.

225 Linear Algebra with Modern Applications 3 Course Prerequisite: MATH 106 or higher. Enrollment not allowed if credit already earned for MATH 220 or 230. Solving linear systems, matrices, determinants, subspaces, eigenvalues, orthogonality, machine learning, AI, computer graphics, and economic models. Credit not granted for more than one of MATH 220, 225, and 230.

230 Honors Introductory Linear Algebra 3 Course Prerequisite: MATH 171 or concurrent enrollment. Enrollment not allowed if credit already earned for MATH 220 or 225. An introduction to linear algebra with an emphasis on conceptual development. Credit not granted for more than one of MATH 220, 225, and 230.

251 Fundamentals of Elementary Mathematics I 3 (2-2) Course Prerequisite: MATH 101, 103, 105, 106, or 201, each with a C or better, or STAT 212 with a C or better, or a minimum ALEKS math placement score of 45%. Comprehensive development of number systems emphasizing place-value, integers, rational numbers, and associated algorithms; methods of problem solving.

251 (Effective through Summer 2021) Fundamentals of Elementary Mathematics I 3 (2-2) Course Prerequisite: MATH 101, 103, 105, or 106, each with a C or better, or STAT 212 with a C or better, or a minimum ALEKS math placement score of 45%. Comprehensive development of number systems emphasizing place-value, integers, rational numbers, and associated algorithms; methods of problem solving.

252 [QUAN] Fundamentals of Elementary Mathematics II 3 (2-2) Course Prerequisite: MATH 251 with a C or better. Inquiry-based approach to fundamental concepts: measurement, geometrical constructions, similarity, congruence, symmetry, probability, counting principles, measures of central tendency, and distributions. Required preparation: One year of high school geometry.

273 Calculus III 2 Course Prerequisite: MATH 172 with a C or better, or MATH 182 with a C or better. Calculus of functions of several variables. Credit not granted for both MATH 273 and 283.

283 Honors Calculus III 2 Course Prerequisite: MATH 182 or by department permission. Multivariable calculus with emphasis on conceptual development and problem solving. Credit not granted for both MATH 273 and 283.

300 Mathematical Computing 3 Course Prerequisite: MATH 220, 225, or 230; admitted to the major in Mathematics. Examination of some current computer software for solving mathematical problems. Recommended preparation: MATH 315.

300 (Effective through Summer 2021) Mathematical Computing 3 Course Prerequisite: MATH 220 or MATH 230. Examination of some current computer software for solving mathematical problems. Recommended preparation: MATH 315.

301 Introduction to Mathematical Reasoning 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better. Mathematical arguments and the writing of proofs.

301 (Effective through Summer 2021) Introduction to Mathematical Reasoning 3 Course Prerequisite: MATH 220 with a C or better, or MATH 230 with a C or better. Mathematical arguments and the writing of proofs.

302 Theory of Numbers 3 Course Prerequisite: MATH 172 with a C or better, or MATH 182 with a C or better; MATH 301 with a C or better. Divisibility properties of integers; congruences; Diophantine equations; quadratic residues.

303 [M] Geometry for the Middle School Teacher 3 Course Prerequisite: MATH 252. Topics in 2D and 3D geometry including technology-based reasoning and exploration, deductive arguments, transformational and proportional reasoning, and non-Euclidean geometries.

315 Differential Equations 3 Course Prerequisite: MATH 273 or 283, each with a C or better; and MATH 220, 225, or 230, each with a C or better, or concurrent enrollment. Linear differential equations and systems; series, numerical and qualitative approaches; applications.

315 (Effective through Summer 2021) Differential Equations 3 Course Prerequisite: MATH 273 with a C or better or Math 283 with a C or better; and MATH 220 with a C or better or concurrent enrollment, or MATH 230 with a C or better or concurrent enrollment. Linear differential equations and systems; series, numerical and qualitative approaches; applications.

320 [M] Elementary Modern Algebra 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better; MATH 301. Algebra as a deductive system; number systems; groups, rings, and fields.

320 (Effective through Summer 2021) [M] Elementary Modern Algebra 3 Course Prerequisite: MATH 220 with a C or better or MATH 230 with a C or better. Algebra as a deductive system; number systems; groups, rings, and fields.

325 Elementary Combinatorics 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better. Introduction to combinatorial theory: counting methods, binomial coefficients and identities, generating functions, occurrence relations, inclusion-exclusion methods.

325 (Effective through Summer 2021) Elementary Combinatorics 3 Course Prerequisite: MATH 220 with a C or better or MATH 230 with a C or better. Introduction to combinatorial theory: counting methods, binomial coefficients and identities, generating functions, occurrence relations, inclusion-exclusion methods.

330 Methods of Teaching Secondary School Mathematics 3 Course Prerequisite: MATH 301 or concurrent enrollment. New curricula and pedagogical techniques for secondary school mathematics.

340 Introduction to Mathematical Biology 3 Course Prerequisite: MATH 140 with a C or better, or MATH 172 with a C or better, or MATH 182 with a C or better; BIOLOGY 101, BIOLOGY 102, BIOLOGY 106, or BIOLOGY 107. Mathematical biology and development of mathematical modeling for solutions to problems in the life sciences. (Crosslisted course offered as MATH 340, BIOLOGY 340).

351 Algebraic Thinking for the Middle School Teacher 3 Course Prerequisite: MATH 252 with a C or better. Algebraic reasoning, classes of functions, translation among models, analytical rule, tables of data, context and coordinate graphs.

352 Probability and Data Analysis for Middle School Teachers 3 Course Prerequisite: MATH 251 and 252; or STAT 360. Probability and statistics in relation to middle school mathematics and real world problems through visualization, hands-on activities, and technology.

352 (Effective through Fall 2021) Probability and Data Analysis for Middle School Teachers 3 Course Prerequisite: MATH 251; MATH 252. Probability and statistics in relation to middle school mathematics and real world problems through visualization, hands-on activities, and technology.

364 Principles of Optimization 3 Course Prerequisite: MATH 202, 220, 225, or 230. Algebra of linear inequalities; duality; graphs, transport networks; linear programming; special algorithms; nonlinear programming; selected applications.

364 (Effective through Summer 2021) Principles of Optimization 3 Course Prerequisite: MATH 202, MATH 220, or MATH 230. Algebra of linear inequalities; duality; graphs, transport networks; linear programming; special algorithms; nonlinear programming; selected applications.

375 Vector Analysis 3 Course Prerequisite: MATH 315. Line integrals, gradient, curl, divergence; Stokes' theorem, potential functions.

398 Mathematical Snapshots 1 Course Prerequisite: MATH 172 or MATH 182. Character, life work, and historical importance of mathematicians from various eras and branches of mathematics.

401 [M] Introduction to Analysis I 3 Course Prerequisite: MATH 301 with a C or better. Properties of sets and sequences of real numbers; limits, continuity, differentiation and integration of functions; metric spaces.

402 [M] Introduction to Analysis II 3 Course Prerequisite: MATH 401. Sequences of functions, power series, multivariable calculus, inverse and implicit function theorems, Lagrange multipliers, change of variable in multiple integrations.

403 Euclidean and Non-Euclidean Geometry 3 Course Prerequisite: MATH 301 with a C or better. Geometry as a deductive system of logic; postulational systems; projective and non-Euclidian geometries.

405 Introduction to Financial Mathematics 3 Course Prerequisite: MATH 172 or 182. Introduction to financial mathematics including the basics of annuities, stocks, bonds, and financial derivatives.

415 Intermediate Differential Equations 3 Course Prerequisite: MATH 315. Linear systems; qualitative theory (existence, uniqueness, stability, periodicity); boundary value problems; applications.

416 Numerical Simulations for Probabilistic Models 3 Course Prerequisite: STAT 360; CPT S 121, CPT S 251, or MATH 300. Efficient generation of random variables; statistical analysis and validation techniques; variance reduction; Markov Chain Monte Carlo methods; applications include complex systems, financial models, and Bayesian computation. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

420 Linear Algebra 3 Course Prerequisite: MATH 220, 225, or 230, each with a C or better; MATH 301 with a C or better. Vector spaces, linear transformations, diagonalizability, normal matrices, inner product spaces, orthogonality, orthogonal projections, least-squares, SVD.

420 (Effective through Summer 2021) Linear Algebra 3 Course Prerequisite: MATH 220 with a C or better, or MATH 230 with a C or better; MATH 301 with a C or better. Vector spaces, linear transformations, diagonalizability, normal matrices, inner product spaces, orthogonality, orthogonal projections, least-squares, SVD.

421 [M] Algebraic Structures 3 Course Prerequisite: MATH 301 with a C or better. Properties of algebraic structures and their homomorphisms, semi-groups, groups, rings, unique factorization domains, fields.

425 Conceptual Aspects of Mathematics 3 Course Prerequisite: By instructor permission. Exploration of conceptual models for thinking about mathematical ideas; activities and discussions of mathematical thinking and instruction. (Crosslisted course offered as TCH LRN 425, MATH 425).

431 Intersections of Culture and Mathematics 3 Course Prerequisite: MATH 301 with a C or better. Gender/race/ethnicity differences; social consequences; cultural influences on development and learning of mathematics; role of women, people of color in mathematics. Credit not granted for both MATH 431 and 531. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

432 [CAPS] Mathematics for College and Secondary Teachers 3 Course Prerequisite: MATH 301 with a C or better. Pre-algebra, algebra functions and geometry examined from an advanced perspective, for secondary and lower level college teachers.

440 Applied Mathematics I: PDEs 3 Course Prerequisite: MATH 315. Applied partial differential equations; Fourier series; Bessel functions and Legendre polynomials as harmonics for disks and balls; Laplace, heat, and wave equations; separation of variables and D'Alambert's formula. Credit not granted for both MATH 440 and MATH 540. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

441 Applied Mathematics II: Complex Variables 3 Course Prerequisite: MATH 315. Complex numbers and complex-valued functions of one complex variable; analytic functions and Cauchy-Riemann equations; differentiation and contour integration; Cauchy integral theorem; Taylor and Laurent series; residues; conformal mapping; applications to potential theory. Credit not granted for both MATH 441 and MATH 541. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

448 Numerical Analysis 3 Course Prerequisite: MATH 315 with a C or better; one of CPT S 121, 131, or MATH 300, with a C or better. Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. (Crosslisted course offered as MATH 448, MATH 548, CPT S 430, CPT S 530). Required preparation must include differential equations and a programming course. Offered at 400 and 500 level.

453 Graph Theory 3 Course Prerequisite: MATH 220, 225, or 230. Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Recommended preparation: MATH 301. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

453 (Effective through Summer 2021) Graph Theory 3 Course Prerequisite: MATH 220 or MATH 230. Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Recommended preparation: MATH 301. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

456 Introduction to Statistical Theory 3 Course Prerequisite: STAT 430 or 443. Sampling distributions; hypothesis testing and estimation; maximum likelihood; likelihood ratio tests; theory of least squares; nonparametrics. (Crosslisted course offered as STAT 456, MATH 456). Credit not granted for more than one of STAT/MATH 456 or STAT 556. Recommended preparation: One 3-credit 400-level STAT or probability course. Offered at 400 and 500 level.

464 [CAPS] Linear Optimization 3 Course Prerequisite: MATH 273 or MATH 283. Linear and integer programming; optimization problems; applications to economic and military strategies; rectangular games; minimax theory. Recommended preparation: MATH 301.

466 Optimization in Networks 3 Course Prerequisite: MATH 364. Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman, and salesman. Credit not granted for both MATH 466 and MATH 566. Required preparation must include linear programming. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

486 Mathematical Methods in Natural Sciences 3 Course Prerequisite: MATH 315. Introduction to mathematical modeling of natural processes; methods include dimensional and scaling analysis, perturbation theory, field theory of continuum mechanics, calculus of variations, and Markov chains; applications to physics, chemistry, biology, and engineering. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

490 Topics in Mathematics V 1-3 May be repeated for credit; cumulative maximum 9 hours. Course Prerequisite: By instructor permission. Special topics in mathematics.

494 Seminar in Mathematical Biology 1 May be repeated for credit; cumulative maximum 4 hours. Course Prerequisite: MATH 140 with a C or better, or MATH 172 with a C or better, or MATH 182 with a C or better; BIOLOGY 101, BIOLOGY 102, BIOLOGY 106, or BIOLOGY 107. Oral presentation of research approaches, research results and literature review of mathematical biology including mathematical modeling of biological systems. (Crosslisted course offered as MATH 494, BIOLOGY 494). Cooperative: Open to UI degree-seeking students. S, F grading.

497 Instructional Practicum V 1-2 May be repeated for credit; cumulative maximum 2 hours. Course Prerequisite: By instructor permission. S, F grading.

499 Special Problems V 1-4 May be repeated for credit. Independent study conducted under the jurisdiction of an approving faculty member; may include independent research studies in technical or specialized problems; selection and analysis of specified readings; development of a creative project; or field experiences. S, F grading.

500 Proseminar 1 May be repeated for credit; cumulative maximum 2 hours. S, F grading.

501 Real Analysis 3 Metric spaces, convergence, continuous functions, infinite series, differentiation and integration of functions of one and several variables. Required preparation must include advanced calculus or real analysis.

502 Introduction to Functional Analysis 3 Course Prerequisite: MATH 501. Normed linear spaces, Banach spaces, introduction to Hilbert space, linear operators. Required preparation: Advanced linear algebra.

503 Complex Analysis 3 Course Prerequisite: MATH 501. Analytic functions, complex integration, Taylor and Laurent series, conformal mapping, Riemann surfaces and analytic continuation. Cooperative: Open to UI degree-seeking students.

504 Measure and Integration 3 Course Prerequisite: MATH 501. Lebesque measure, Lebesque integration, differentiation, L spaces, general measure and integration, Radon-Nikodym Theorem, outer measure and product measures. Cooperative: Open to UI degree-seeking students.

505 Abstract Algebra 3 Groups, rings, fields, and homological algebra. Required preparation must include abstract algebra. Cooperative: Open to UI degree-seeking students.

507 Advanced Theory of Numbers 3 May be repeated for credit; cumulative maximum 6 hours. Analytic and algebraic number theory. Cooperative: Open to UI degree-seeking students.

508 Advanced Mathematical Methods for Physics and Engineering 3 Advanced treatment of applications using techniques from fundamental analysis, convexity, analytic function theory, asymptotics, and differential equations. Cooperative: Open to UI degree-seeking students.

511 Advanced Linear Algebra 3 Spectral theory, Schur's theorem, normality, Jordan canonical forms, hermitian matrices, variational inequalities, matrix norms, eigenvalue localization, matrix perturbation theory. Required preparation must include second level undergraduate linear algebra. Cooperative: Open to UI degree-seeking students.

512 Ordinary Differential Equations 3 Existence of solutions; linear systems; qualitative behavior, especially stability; periodic solutions. Required preparation must include a year-long sequence in advanced calculus or real analysis. Cooperative: Open to UI degree-seeking students.

516 Numerical Simulations for Probabilistic Models 3 Efficient generation of random variables; statistical analysis and validation techniques; variance reduction; Markov Chain Monte Carlo methods; applications include complex systems, financial models, and Bayesian computation. Credit not granted for both MATH 416 and MATH 516. Required preparation must include probability and statistics and programming experience. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

524 Algebraic Topology 3 Algebraic techniques (groups, homomorphisms, etc) to study connectivity of spaces; topics include simplicial complexes, homology, relative homology, Meyer-Vietoris sequences, categories and functors, cohomology, and duality in manifolds. Recommended preparation: real analysis and abstract algebra.

525 General Topology 3 Sets, metric spaces, topological spaces; continuous mappings, compactness, connectedness, local properties, function spaces, and fundamental groups. Required preparation must include a year-long sequence in advanced calculus or real analysis. Cooperative: Open to UI degree-seeking students.

529 Computational Topology 3 Topological techniques combined with algorithms to find structure in data; simplicial complexes from point clouds, algorithms for homology and persistent homology, mapper and topological data analysis, optimal homology problems. Recommended preparation: mathematical maturity at senior undergraduate level and some experience with computer programming.

531 Intersections of Culture and Mathematics 3 Gender/race/ethnicity differences; social consequences; cultural influences on development and learning of mathematics; role of women, people of color in mathematics. Credit not granted for both MATH 431 and 531. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

532 Advanced Mathematical Thinking 3 Course Prerequisite: Graduate standing in mathematics. Current theories about how humans learn to think mathematically at the advanced level. Cooperative: Open to UI degree-seeking students.

533 Teaching College Mathematics 1 May be repeated for credit; cumulative maximum 3 hours. Course Prerequisite: Graduate standing in Mathematics or Statistical Science. Theory and practice of mathematics instruction at the collegiate level.

534 Theories of Learning in Mathematics 3 Math learning theories, including behaviorism, information processing, constructivism, situated cognition, communities of practice; influence on teaching and learning mathematics. Cooperative: Open to UI degree-seeking students.

535 Research Paradigms in Mathematics Education 3 Course Prerequisite: MATH 534. Current research paradigms in math education research; critique research designs used in current mathematics education research article; design and carry out a research project. Cooperative: Open to UI degree-seeking students.

536 Statistical Computing 3 (2-3) Course Prerequisite: STAT 556. Generation of random variables, Monte Carlo simulation, bootstrap and jackknife methods, EM algorithm, Markov chain Monte Carlo methods. (Crosslisted course offered as STAT 536, MATH 536). Recommended preparation: One 3-credit 400-level probability or STAT course. Cooperative: Open to UI degree-seeking students.

540 Applied Mathematics I: PDEs 3 Applied partial differential equations; Fourier series; Bessel functions and Legendre polynomials as harmonics for disks and balls; Laplace, heat, and wave equations; separation of variables and D'Alambert's formula. Credit not granted for both MATH 440 and MATH 540. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

541 Applied Mathematics II: Complex Variables 3 Complex numbers and complex-valued functions of one complex variable; analytic functions and Cauchy-Riemann equations; differentiation and contour integration; Cauchy integral theorem; Taylor and Laurent series; residues; conformal mapping; applications to potential theory. Credit not granted for both MATH 441 and MATH 541. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

543 Stable Numerical Methods Using Orthogonality 3 Computational methods for stabilizing difficult and ill-posed differential and integral equations problems by using systems of functions and regularization techniques; applications to forward and inverse problems; techniques include the use of wavelets and orthogonal polynomials. Required preparation must include numerical analysis. Cooperative: Open to UI degree-seeking students.

544 Advanced Matrix Computations 3 Advanced topics in the solution of linear systems, singular value decomposition, and computation of eigenvalues and eigenvectors (Francis's algorithm). (Crosslisted course offered as MATH 544, CPT S 531). Required preparation must include numerical analysis. Cooperative: Open to UI degree-seeking students.

545 Numerical Analysis of Parabolic and Hyperbolic PDEs 3 Numerical solutions of parabolic and hyperbolic partial differential equations with emphasis on finite difference methods; topics include: finite difference; stability, consistency, and convergence; shocks; conservation of forms. Required preparation must include numerical analysis. Cooperative: Open to UI degree-seeking students.

546 Numerical Analysis of Elliptic PDEs 3 Numerical solutions of elliptic partial differential equations with emphasis on finite element methods; finite difference; error analysis. Required preparation must include numerical analysis. Cooperative: Open to UI degree-seeking students.

548 Numerical Analysis 3 Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. (Crosslisted course offered as MATH 448, MATH 548, CPT S 430, CPT S 530). Required preparation must include differential equations and a programming course. Offered at 400 and 500 level.

553 Graph Theory 3 Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Recommended preparation: MATH 301. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

553 (Effective through Summer 2021) Graph Theory 3 Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. (Crosslisted course offered as MATH 453, MATH 553, CPT S 453, CPT S 553). Required preparation must include linear algebra. Recommended preparation: MATH 301. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

555 Topics in Combinatorics 3 May be repeated for credit; cumulative maximum 6 hours. Combinatorics, generating functions, recurrence relations, inclusion-exclusion, coding theory; experimental design, graph theory. Cooperative: Open to UI degree-seeking students.

560 Partial Differential Equations I 3 Partial differential equations and other functional equations: general theory, methods of solution, applications. Required preparation must include a year-long sequence in advanced calculus or real analysis. Cooperative: Open to UI degree-seeking students.

561 Partial Differential Equations II 3 Course Prerequisite: MATH 560. Continuation of MATH 560. Cooperative: Open to UI degree-seeking students.

563 Mathematical Genetics 3 Mathematical approaches to population genetics and genome analysis; theories and statistical analyses of genetic parameters. (Crosslisted course offered as MATH 563, BIOLOGY 566). Required preparation must include multivariate calculus, genetics, and statistics. Cooperative: Open to UI degree-seeking students.

564 Convex and Nonlinear Optimization 3 Convex sets and functions; operations preserving convexity; linear, quadratic, and conic optimization; duality theory; unconstrained smooth optimization; interior point methods. Required preparation must include advanced multivariate calculus, and a programming language. Recommended preparation: Knowledge in linear optimization and numerical linear algebra. Cooperative: Open to UI degree-seeking students.

565 Nonsmooth Analysis and Optimization with Applications 3 Course Prerequisite: MATH 564. Extended real-valued functions; continuity and convexity; subgradient, conjugate functions and optimality condition; alternating minimization; projected subgradient methods; alternating direction methods of multipliers; applications in statistical learning. Required preparation must include real analysis and command of a programming language. Cooperative: Open to UI degree-seeking students.

566 Optimization in Networks 3 Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman, and salesman. Credit not granted for both MATH 466 and MATH 566. Required preparation must include linear programming. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

567 Integer and Combinatorial Optimization 3 Theory and applications of integer and combinatorial optimization including enumerative, cutting plane, basis reduction, relaxation and matching methods. Required preparation must include linear optimization. Cooperative: Open to UI degree-seeking students.

568 Statistical Theory I 3 Probability spaces, combinatorics, multidimensional random variables, characteristic function, special distributions, limit theorems, stochastic processes, order statistics. (Crosslisted course offered as STAT 548, MATH 568). Recommended preparation: Calculus III and one 3-credit 400-level probability course. Cooperative: Open to UI degree-seeking students.

569 Statistical Theory II 3 Course Prerequisite: STAT 548 or MATH 568. Statistical inferences; estimation and testing hypotheses; regression analysis; sequential analysis and nonparametric methods. (Crosslisted course offered as STAT 549, MATH 569). Cooperative: Open to UI degree-seeking students.

570 Continuum Mechanics 3 Unified presentation of principles common to all branches of solid and fluid mechanics; viscous fluids, elasticity, viscoelasticity, and plasticity. (Crosslisted course offered as ME 501, MATH 570.) Cooperative: Open to UI degree-seeking students.

571 Mathematical Foundations of Continuum Mechanics II 3 Course Prerequisite: MATH 570. Continuation of MATH 570. Cooperative: Open to UI degree-seeking students.

574 Topics in Optimization 3 May be repeated for credit; cumulative maximum 12 hours. Advanced topics in the theory and computing methodology in optimization with emphasis on real-life algorithmic implementations. Required preparation must include advanced multivariable calculus and a programming language. Cooperative: Open to UI degree-seeking students.

575 Asset Pricing in Financial Engineering 3 Mathematical methods for various models on valuation of stocks and options, with rigorous mathematical analysis on pricing and hedging techniques. Recommended preparation: Advanced calculus and some knowledge on differential equations. Cooperative: Open to UI degree-seeking students.

576 Quantitative Risk Management 3 Fundamental concepts in modern risk theory and mathematical methods in quantitative risk management; coherent risk measures, volatility modeling, multivariate dependence analysis using copulas, risk aggregation and allocation, and extreme value theory. Cooperative: Open to UI degree-seeking students.

579 Mathematical Modeling in the Biological and Health Sciences 3 Techniques, theory, and current literature in mathematical modeling in the biological and health sciences, including computational simulation. (Course offered as BIOLOGY 579, MATH 579). Cooperative: Open to UI degree-seeking students.

581 Topics in Mathematics V 1-3 May be repeated for credit. Topics in mathematics. Cooperative: Open to UI degree-seeking students.

583 Topics in Applied Mathematics V 1-3 May be repeated for credit. Topics in applied mathematics. Cooperative: Open to UI degree-seeking students.

586 Mathematical Methods in Natural Sciences 3 Introduction to mathematical modeling of natural processes; methods include dimensional and scaling analysis, perturbation theory, field theory of continuum mechanics, calculus of variations, and Markov chains; applications to physics, chemistry, biology, and engineering. Credit not granted for both MATH 486 and MATH 586. Required preparation must include differential equations. Offered at 400 and 500 level. Cooperative: Open to UI degree-seeking students.

587 Topics in Algebra and Linear Algebra V 1-3 May be repeated for credit. Advanced topics in algebra and linear algebra. Recommended preparation: Two semesters of linear algebra and one semester of abstract algebra.

588 Topics in Computational Math V 1-3 May be repeated for credit. Advanced topics in computational mathematics. Recommended preparation: one semester of numerical analysis.

588 (Effective through Summer 2021) Topics in Computational Math V 1-3 May be repeated for credit. Advanced topics in algebra and linear algebra. Recommended preparation: one semester of numerical analysis.

589 Topics in Analysis V 1-3 Advanced topics in mathematical analysis. Recommended preparation: one semester of graduate analysis.

590 Topics in Mathematics Education V 1-3 May be repeated for credit; cumulative maximum 6 hours. Topics in mathematics education.

591 Seminar in Mathematical Biology 1 May be repeated for credit; cumulative maximum 10 hours. Current research in mathematical biology. S, F grading.

592 Seminar in Analysis 1 May be repeated for credit; cumulative maximum 10 hours. Current research in analysis. S, F grading.

593 Seminar in Combinatorics, Linear Algebra, and Number Theory 1 May be repeated for credit; cumulative maximum 10 hours. Current research in combinatorics, linear algebra, and number theory. S, F grading.

594 Mathematics Education Seminar 1 May be repeated for credit; cumulative maximum 10 hours. Current research in mathematics education. S, F grading.

597 Mathematics Instruction Seminar 1 May be repeated for credit; cumulative maximum 5 hours. Introduction to the teaching of university mathematics. S, F grading.

600 Special Projects or Independent Study V 1-18 May be repeated for credit. Independent study, special projects, and/or internships. Students must have graduate degree-seeking status and should check with their major advisor before enrolling in 600 credit, which cannot be used toward the core graded credits required for a graduate degree. S, F grading.

702 Master's Special Problems, Directed Study, and/or Examination V 1-18 May be repeated for credit. Independent research in special problems, directed study, and/or examination credit for students in a non-thesis master's degree program. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 702 credit. S, U grading.

800 Doctoral Research, Dissertation, and/or Examination V 1-18 May be repeated for credit. Course Prerequisite: Admitted to the Mathematics PhD program. Independent research and advanced study for students working on their doctoral research, dissertation and/or final examination. Students must have graduate degree-seeking status and should check with their major advisor/committee chair before enrolling for 800 credit. S, U grading.

- Mathematics and Statistics
### Courses

- Mathematics
- Statistics
### Schedules of Studies

- Actuarial Science Option
- Applied Option
- Secondary Teaching Option with Certification
- Secondary Teaching Option Without Certification
- Statistics Option
- Theoretical Option
### Minors

- Statistics
- Mathematics
### Certificates

- Certificate in Quantitative Biology